Method and apparatus for non-invasive blood constituent monitoring

ABSTRACT

A system for determining a biologic constituent including hematocrit transcutaneously, noninvasively and continuously. A finger clip assembly includes including at least a pair of emitters and a photodiode in appropriate alignment to enable operation in either a transmissive mode or a reflectance mode. At least one predetermined wavelength of light is passed onto or through body tissues such as a finger, earlobe, or scalp, etc. and attenuation of light at that wavelength is detected. Likewise, the change in blood flow is determined by various techniques including optical, pressure, piezo and strain gage methods. Mathematical manipulation of the detected values compensates for the effects of body tissue and fluid and determines the hematocrit value. If an additional wavelength of light is used which attenuates light substantially differently by oxyhemoglobin and reduced hemoglobin, then the blood oxygen saturation value, independent of hematocrit may be determined. Further, if an additional wavelength of light is used which greatly attenuates light due to bilirubin (440 nm) or glucose (1060 nm), then the bilirubin or glucose value may also be determined. Also how to determine the hematocrit with a two step DC analysis technique is provided. Then a pulse wave is not required, so this method may be utilized in states of low blood pressure or low blood flow.

BACKGROUND

[0001] The present invention is related to U.S. Pat. Nos. 5,372,136 and5,499,627 the text and drawings of which are incorporated herein byreference as if reproduced in full.

[0002] 1. The Field of the Invention

[0003] The present invention relates to improvements in the systems andmethods for non-invasively measuring one or more biologic constituentconcentration values. More particularly, the present invention relatesto non-invasive spectrophotometric systems and methods forquantitatively and continuously monitoring the hematocrit and otherblood parameters.

[0004] 2. The Prior Art

[0005] Modern medical practice utilizes a number of procedures andindicators to assess a patient's condition. One of these indicators isthe patient's hematocrit. Hematocrit (often abbreviated as HCT) is thevolume expressed as a percentage of the patient's blood which isoccupied by red corpuscles, commonly referred to as red blood cells. Thepresent invention is presented in the context of hematocrit. However, itis to be understood that the teachings of the present invention apply toany desired biologic constituent parameter.

[0006] Medical professionals routinely desire to know the hematocrit ofa patient. In order to determine hematocrit using any of the techniquesavailable to date, it is necessary to draw a sample of blood bypuncturing a vein or invading a capillary. Then, using widely acceptedtechniques, the sample of blood is subjected to either high-speedcentrifuge, cell counting, ultrasonic, conductometric or photometricmethods of evaluating the sample of blood in a fixed container. PriorU.S. Pat. No. 5,372,136 indicates a system and methodology fordetermining the hematocrit non-invasively, without puncturing orinvading the body, spectrophotometrically and continuously in a subject.The present invention relates to improvements upon the above citedsystem.

[0007] Beyond the above referenced patent, others have suggested variousmeans of noninvasive measurement of hematocrit. Specifically, Mendelson,U.S. Pat. No. 5,277,181; Seeker, U.S. Pat. No. 5,188,108; Gonatas, U.S.Pat. No. 5,528,365; Ishikawa, U.S. Pat. No. 5,522,388; Shiga, U.S. Pat.No. 4,927,264; Tsuchiya, U.S. Pat. Nos. 5,441,054, 5,529,065, 5,517,987and 5,477,051; and Chance, U.S. Pat. Nos. 5,353,799, 5,402,778, and5,673,701 have attempted to define means of directly measuring desiredbiologic constituents such as hematocrit. Even though the variouspatents indicate the need to utilize multiple wavelengths measured atdifferent detection sites and/or the need to perform differential orratiometric operations on the detected optical signal, all fail toisolate and resolve the individual and specific scattering andabsorption coefficients of the desired constituent. At best they addressonly bulk attenuation coefficients and/or bulk diffusion constants ofthe scattering media while attempting to resolve such constraints astissue nonhomogeneity. As an example, tissue may be considered tocontain a bulk absorptive coefficient due to blood, collagen, water,fibers, bone, fingernail, etc. Hence, in order to determine theabsorptive coefficient of the blood itself, the bulk value of the tissueper se must be prorated by the amounts of the above constituents.Secondly, the actual absorptive coefficient of the blood must then bedecoupled or isolated from its proration factor as well.

OBJECTS OF THE INVENTION

[0008] Thus, it is an object of the present invention to provide animprovement in the systems and methods for the non-invasive(transcutaneous) and continuous determination of the blood Hematocrit inliving tissue.

[0009] It is yet another object of the present invention to provide animprovement in the systems and methods for the non-invasive(transcutaneous) and continuous determination of the blood constituents,including glucose, bilirubin, cholesterol, tissue water, etc. in livingtissue.

[0010] It is another object of the present invention to provide a systemand method and apparatus for the display of both immediate and/orcontinuous visual information regarding the HCT of the subject.

[0011] It is yet another object of the present invention to provide arepeatable and reliable method and apparatus for the non-invasivedetermination of hematocrit transcutaneously and in real time even undervarying physiological conditions.

[0012] Still another object of the present invention is to provide amethod and apparatus for the instantaneous determination of the bulkabsorption coefficient of the scattering media.

[0013] These and other objects and advantages of the invention willbecome more fully apparent from the description in the specification andclaims, which follow.

SUMMARY OF THE INVENTION

[0014] In one aspect, the present invention accomplishes thetranscutaneous, noninvasive, real-time and continuous measurement of thehematocrit and other blood constituents of the patient. That is, theelectronic circuitry necessary is included to receive signals from adetector and to generate appropriate signals at various input sites asdescribed in U.S. Pat. No. 5,372,136. Yet another aspect of the presentinvention is the ability to extract the blood absorption coefficientfrom the bulk tissue diffusion constant or the bulk absorptioncoefficient of the scattering media by requiring both physical andmathematical operations.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015]FIGS. 1 and 1A show a finger placed into a clam-shell type fixtureconstituting a receiving means for detector and emitter arrays operatingin a transmission mode and the blood conduit which in the figures is thefinger.

[0016]FIGS. 1B and 1C are similar to FIG. 1A, but show the detector andemitter arrays operating in a reflectance mode.

[0017]FIG. 1D is a schematic diagram for a mylar base with a detector,emitters and either a strain gage or a pressure transducer for inclusionin the clam-shell fixture.

[0018]FIG. 1E is a schematic diagram for a detector emitter array usinga single, moveable emitter in a transmission mode.

[0019]FIG. 2 shows actual patient data plot of ln(i) vs. d.

[0020]FIG. 3 illustrates actual patient data of the (∂i/∂t)/i dependenceon d.

[0021]FIG. 4 shows the blood absorption coefficient's dependence onhematocrit.

[0022]FIG. 5 indicates the nonlinear relationship between theV_(c)/V_(ƒ)and pressure.

[0023]FIG. 6 shows the electrical circuit diagram of the piezofilm/strain gage transducer means.

[0024]FIG. 7 is the plot of ƒ(H) vs. measured Hematocrit.

[0025]FIG. 8 shows the instantaneous time derivatives of (∂i/∂t)/i and a∂P/∂t versus time during one cardiac pulse.

[0026]FIG. 9 plots (∂i/∂t)/i versus ∂P/∂t for a given human pulse at d₁,d₂, d₃, and d₄.

[0027]FIG. 10 plots (∂i/∂t)/ (∂P/∂t) versus time during a single cardiacpulse cycle.

[0028]FIG. 11 is the circuit diagram of the pressure transducer means.

[0029]FIG. 12 plots α versus X_(b) at a fixed Hematocrit.

[0030]FIG. 13 gives the patient data of the new transcutaneousHematocrit method and system plotted versus the measured Hematocritstandard.

DETAILED DESCRIPTION OF THE INVENTION

[0031] In a preferred embodiment of the invention, measurements areconducted using a modified version of the apparatus described in U.S.Pat. Nos. 5,456,253 and 5,372,136, both of which are incorporated hereinas if reproduced in full below. Both of these patents form part of thepresent disclosure.

[0032] Thus, in a preferred embodiment, hematocrit is measured in livingtissue located at some convenient location on the body, such as, an earlobe, finger tip, nose or other accessible tissue sites. In a preferredembodiment the apparatus and signal manipulations described in U.S. Pat.No. 5,372,136 are utilized to measure various optical parameters thatwill be described hereafter. The numbered components in FIGS. 1, 1A, 1B,and 1C are similar to the numbers in FIG. 1 of U.S. Pat. No. 5,456,253.

[0033] In the present disclosure, FIG. 1 shows the finger 7 of anindividual placed into a clam-shell type fixture 6 wherein the opticaland other physical measurements can be easily performed. The clam-shelltype holder allows for adaptability to various finger sizes. However,other fixture methods such as FIGS. 1B through 1E, can be used to obtainsimilar physical data as using the clam-shell fixture.

THEORETICAL BASIS OF THE SPECTROPHOTOMETRIC AND MATHEMATICAL ANALYSISFOR TRANSCUTANEOUS HEMATOCRIT MEASUREMENT

[0034] Non-invasive, transcutaneous hematocrit measurement using aspectroscopic method is described below:

[0035] I. Introduction

[0036] Earlier spectrophotometric techniques have fallen short of beingable to fully characterize the individual blood absorbance coefficients.The following discussion demonstrates the method of decoupling, orisolating from the bulk tissue attenuation parameters (including theconvoluted absorptive and scattering parameters) the individual bloodabsorptive constants. This unique method identifies, isolates andcompartmentalizes each of the contributing biologic elements of thetissue media. This decoupling process can either isolate the bloodabsorbance of interest and/or eliminate the scattering contribution fromthe bulk media measurement.

[0037] From photon diffusion analysis: $\begin{matrix}{{{{\frac{\partial^{2}}{\partial\rho^{2}}{\Psi (\rho)}} - {a^{2}{\Psi (\rho)}}} = \frac{S(\rho)}{D}}{{where},}} & (1) \\{D = \frac{1}{3\left( {K + S} \right)}} & (2) \\{\alpha = \sqrt{3{K\left( {K + S} \right)}}} & (3) \\{K = {{K_{b}X_{b}} + {K_{s}X_{s}} + {K_{w}X_{w}}}} & (4) \\{K_{b} = {{\frac{H}{V}\left( {{\sigma_{ao}{SAT}} + {\left( {1 - {SAT}} \right)\sigma_{ar}}} \right)} + {\left( {1 - H} \right)K_{p}}}} & (5) \\{S = {{S_{b}X_{b}} + {S_{s}X_{s}}}} & (6) \\{S_{b} = \frac{\sigma_{s}{H\left( {1 - H} \right)}\left( {1.4 - H} \right)}{V}} & (7)\end{matrix}$

[0038] and where,

[0039] α=Bulk attenuation coefficient of the tissue sample

[0040] K=Bulk absorption coefficient of the tissue sample

[0041] S=Bulk scattering coefficient of the tissue sample

[0042] D=Diffusion constant

[0043] K_(b)=Macroscopic absorption coefficient for whole blood (WB)

[0044] S_(b)=Macroscopic transport-corrected scattering coefficient forWB

[0045] K_(p)=Macroscopic absorption coefficient for plasma

[0046] K_(s)=Macroscopic absorption coefficient for skin, & other nonwater/blood components

[0047] K_(w)=Macroscopic absorption coefficient for water

[0048] V=Volume of a red blood cell (RBC)

[0049] H=Hematocrit, volume fraction of RBCs to total blood volume

[0050] SAT=Oxygen saturation %

[0051] σ_(ao)=Absorption cross-section of oxygenated RBCs

[0052] σ_(ar)=Absorption cross-section of deoxygenated RBCs

[0053] σ_(s)=Transport-corrected scattering cross-section of RBCs

[0054] X_(b)=Fractional volume of blood per total tissue volume

[0055] X_(s)=Fractional volume of skin, & non water/blood components pertotal tissue volume

[0056] X_(w)=Fractional volume of water per total tissue volume

[0057] ψ(ρ)=The photon density at a distance ρ

[0058] S(ρ)=The source function.

[0059] II. Analysis

[0060] The light flux, or intensity, i, is given by$i = {\frac{D{\partial\Psi}}{\partial\rho}.}$

[0061] When evaluated at p=d, one solution to equation (1) is:$\begin{matrix}{i = \frac{A\quad ^{\alpha \quad d}}{e^{2\quad \alpha \quad d} - 1}} & (8)\end{matrix}$

[0062] where A is a nontrivial function of the tissue scatteringcoefficient, S, the distance, d (if small), and the bulk attenuationcoefficient, α. If αd>>1, then (8) becomes: $\begin{matrix}{{i = {A\quad ^{{- \alpha}\quad d}}}{{{where}\quad A} \approx {\frac{\alpha}{\left\lbrack {d^{n} \cdot \left( {1 - ^{{- 2}\quad \alpha \quad d}} \right)} \right\rbrack}\quad {or}\quad \left( {{1/d^{2}} + {{1/\alpha}\quad d}} \right)}}\quad {{{{for}\quad 0} < n < 2},}} & (9)\end{matrix}$

[0063] where n is the power that d is raised to.

[0064]FIG. 2 shows the actual patient data plot of ln(i) vs. d, where αis determined directly from the slope of the line.

[0065] The attenuation coefficient, α, is a bulk term which encompassesthe attenuation measurement sensitivity to variations in skin color,presence of bone, callous, blood and water content, etc. In addition, αexpresses the optical “path lengthening” effects of both the absorptionand scattering characteristics of the tissue. Therefore, since α is afunction of HCT and the intensity of the transmitted light can bemeasured, the HCT can be calculated by manipulation of the precedingrelationships.

[0066] Beginning with equation (9), the troublesome and complex tissuefunction, A, can be eliminated by taking the logarithm of (9) anddifferentiating with respect to the distance, d. Unfortunately the termX_(b) is not known but changes with time as a result of a patient'scardiac cycle. Therefore, by differentiating with respect to time, thisparameter becomes the time rate of change of blood volume which can beobtained through several methods described below. These time anddistance derivatives may be performed in either order.

[0067] [1] Taking the logarithm of (9) and differentiating with respectto the distance, d, yields: $\begin{matrix}{\alpha = \frac{\partial\left\lbrack {\ln (i)} \right\rbrack}{\partial d}} & (10)\end{matrix}$

[0068] Next the derivative of (10) with respect to time, t, gives:$\begin{matrix}{\frac{\partial\alpha}{\partial t} = \frac{\partial\left( \frac{\partial\left\lbrack {\ln (i)} \right\rbrack}{\partial d} \right)}{\partial t}} & (11)\end{matrix}$

[0069] [2] Alternatively, first differentiate (9) with respect to time,t, to get: $\begin{matrix}{\frac{\partial i}{\partial t} = {{\frac{\partial i}{\partial X_{b}}\quad \frac{\partial X_{b}}{\partial t}} + {\frac{\partial i}{\partial X_{s}}\quad \frac{\partial X_{s}}{\partial t}} + {\frac{\partial i}{\partial X_{w}}\quad \frac{\partial X_{w}}{\partial t}}}} & (12)\end{matrix}$

[0070] When$\frac{\partial i}{\partial X_{s}}\quad \frac{\partial X_{s}}{\partial t}\quad {and}\quad \frac{\partial i}{\partial X_{w}}\quad \frac{\partial X_{w}}{\partial t}$

[0071] are negligible, and normalizing (12) by i yields: $\begin{matrix}{{\frac{{\partial i}/{\partial t}}{i} = {\frac{\partial X_{b}}{\partial t}\left( {{\frac{\partial\alpha}{\partial X_{b}}d} - {\frac{1}{A}\quad \frac{\partial A}{\partial X_{b}}}} \right)\quad {or}}},} & (13) \\{{\frac{{\partial i}/{\partial t}}{i} = {\frac{\partial\alpha}{\partial t}\left( {d - d_{o}} \right)}},{{{where}\quad d_{o}} \approx {\frac{1}{\alpha} - \frac{2d}{^{2\alpha \quad d} - 1}}}} & \text{(13a)}\end{matrix}$

[0072]FIG. 3 plainly demonstrates the offset term when the various graphlines are extrapolated to d=0. The amount of offset is shown along they-axis.

[0073] Next differentiate (13) with respect to distance, d, to eliminatethat offset term to get: $\begin{matrix}{\frac{\partial\left( \frac{{\partial i}/{\partial t}}{i} \right)}{\partial d} = {{\frac{\partial X_{b}}{\partial t}\left( \frac{\partial\alpha}{\partial X_{b}} \right)} = \frac{\partial\alpha}{\partial t}}} & (14)\end{matrix}$

[0074] Equations (3)-(7) are now used to extract the hematocrit from α.Squaring (3) and differentiating with respect to time results in:$\begin{matrix}{{2\alpha \frac{\partial\alpha}{\partial t}} = {3\left\lbrack {{\frac{\partial K}{\partial t}\left( {{2K} + S} \right)} + {K\frac{\partial S}{\partial t}}} \right\rbrack}} & (15)\end{matrix}$

[0075] Substituting the derivatives of (4) and (6) into (15) andrearranging: $\begin{matrix}{\begin{matrix}{\frac{\partial\alpha}{\partial t} = \quad {\frac{3}{2\alpha}\left\lbrack {{\left( {{\frac{\partial X_{b}}{\partial t}K_{b}} + {\frac{\partial X_{s}}{\partial t}K_{s}} + {\frac{\partial X_{2}}{\partial t}K_{w}}} \right)\left( {{2K} + S} \right)} +} \right.}} \\{\quad \left. {K\left( {{\frac{\partial X_{b}}{\partial t}S_{b}} + {\frac{\partial X_{s}}{\partial t}S_{s}}} \right)} \right\rbrack}\end{matrix}{{{at}\quad 805\quad {nm}},{{\frac{\partial X_{b}}{\partial t}K_{b}}\operatorname{>>}{\frac{\partial X_{s}}{\partial t}K_{s}}},{{\frac{\partial X_{b}}{\partial t}K_{b}}\operatorname{>>}{\frac{\partial X_{2}}{\partial t}K_{2}}},{{\frac{\partial X_{b}}{\partial t}S_{b}}\operatorname{>>}{\frac{\partial X_{s}}{\partial t}S_{s}\quad {and}\quad K}}}} & (16)\end{matrix}$

[0076] <<S so that (16) can be simplified to: $\begin{matrix}{\frac{\partial\alpha}{\partial t} = {\frac{3}{2\alpha}\quad \frac{\partial X_{b}}{\partial t}\left( {{K_{b}S} + {KS}_{b}} \right)}} & (17)\end{matrix}$

[0077] By using the 805 nm wavelength the red blood cell absorptioncross-section constants are equal, σ_(oo)=σ_(ar), and K_(p) isnegligible. The hematocrit can then be determined directly from K_(b) as(5) simplifies to: $\begin{matrix}{H = {\frac{V}{\sigma_{2}}K_{b}}} & \text{(17a)}\end{matrix}$

[0078]FIG. 4 shows the linearity of K_(b)(H).

[0079] If K_(b)S >>KS_(b), where S is approximately 1.0/mm in humantissue, then solving (17) for K_(b) and substituting into (17a) gives:$\begin{matrix}{H = \frac{\frac{2V}{3\sigma_{a}}\alpha \frac{\partial\alpha}{\partial t}}{\frac{\partial X_{b}}{\partial t}S}} & (18)\end{matrix}$

[0080] To rewrite in terms of measurable intensity, i, (10) and (14) aresubstituted into (18) to obtain: $\begin{matrix}{H = \frac{\frac{2V}{3\sigma_{a}}\quad \frac{\partial\left\lbrack {\ln (i)} \right\rbrack}{\partial d}\quad \frac{\left. {{\partial\left. \left\lbrack {{\partial i}/{\partial t}} \right. \right)}/i} \right\rbrack}{\partial d}}{\frac{\partial X_{b}}{\partial t}S}} & (19)\end{matrix}$

[0081] If K_(b)S is not >>KS_(b), then substituting (5) and (7) into(17a) and rearranging terms yields: $\begin{matrix}{H = {\frac{2\alpha}{3}\quad {\frac{\partial\alpha}{\partial t}/{\frac{\partial X_{b}}{\partial t}\left\lbrack {{S\frac{\sigma_{a}}{V}} + {K\frac{\sigma_{s}}{V}\left( {1 - H} \right)\quad \left( {1.4 - H} \right)}} \right\rbrack}}}} & \text{(18a)} \\{{{Alternatively}\quad {from}\quad \left( {13a} \right)}:{H \approx \frac{\alpha \cdot \left( {{{\partial i}/{\partial t}}/i} \right)}{\left( {d - d_{o}} \right) \cdot X_{b}^{\prime}}}} & \text{(18b)}\end{matrix}$

[0082] Equation (18a) indicates a small nonlinearity in H may occurbased on the magnitude of K for a given individual.

[0083] It should be reiterated that the change in received intensitywith time is a result of the change in normalized blood volume resultingfrom the cardiac cycle itself as blood pulses through the examinedtissue. As the intensity of the received light is measured, its timerate of change can be calculated. The change with distance can bedetermined by placing multiple emitters (such as 1-4 in FIG. 1A) and/ormultiple detectors such that multiple thicknesses of tissue and hence,lengths of tissue are penetrated.

[0084] To examine $\frac{\partial X_{b}}{\partial t}$

[0085] further, the following can be defined for the illuminated tissue:

[0086] V_(b)=Volume of blood,

[0087] V_(w)=Volume of water, and

[0088] V_(s)=Volume of skin, tissue and other non-water or bloodcomponents.

[0089] By definition, $\begin{matrix}{X_{b} = \frac{V_{b}}{V_{b} + V_{w} + V_{s}}} & (20)\end{matrix}$

[0090] differentiating (20) with respect to time gives: $\begin{matrix}{\frac{\partial X_{b}}{\partial t} = \frac{{\left( {V_{w} + V_{s}} \right)\frac{\partial V_{b}}{\partial t}} - \frac{V_{b}{\partial V_{w}}}{\partial t}}{\left( {V_{b} + V_{w} + V_{s}} \right)^{2}}} & (21)\end{matrix}$

$\begin{matrix}{{{\frac{\partial{Vw}}{\partial t}{\operatorname{<<}\frac{\partial{Vb}}{\partial t}}\quad {and}\quad V_{b}{\operatorname{<<}V_{w}}} + V_{s}},{(21)\quad {simplifies}\quad {to}\text{:}}} & \quad \\{\frac{\partial X_{b}}{\partial t} = \frac{\frac{\partial V_{b}}{\partial t}}{V_{total}}} & (22)\end{matrix}$

[0091] It is emphasized that α is a function of the bulk absorption andscattering coefficients, K and S, as well as hematocrit, H. Further,that K and S are functions of the fractional volumes of eachconstituent, X_(b), X_(s), and X_(w), which must be used to prorate theindividual absorption and scattering coefficients, K_(b), K_(s), K_(w),S_(b) and S_(s). Therefore, the transducer system must be responsive notonly to a change in volume (ΔV) due to the influx of the blood, but mustalso be responsive to the normalized change in volume of blood,normalized to the total volume of the finger (V_(ƒ))or tissue beingmeasured, $\left( \frac{\Delta \quad V_{f}}{V_{f}} \right).$

[0092] For Reflectance (R) measurements in homogenous tissue:

[0093] R=Ae^(−αr), where A≈(1/r²+1/αr), where r is the radial distance,and$\frac{dR}{R} = {\alpha^{\prime}\left( {r/\left( {\alpha^{2} + {\alpha \quad r}} \right)} \right)}$

[0094] However, for tissue, which is typically non-homogeneous with adermal and subcutaneous layer, the reflectance will not be a trivialfunction but can be described as approximately:

R=[(C ₁ +C ₂)exp(−C ₃ ·r)]/r ^(n)

[0095] Where C₁ and C₂ are inter-related photon flux densities betweenthe dermal layer 12 and the subcutaneous layer, 12 a (see FIGS. 1C and1E). Likewise, C₃ is a strong function of z₁, z₂, α₁, and α₂; i.e., thethickness of the dermis or dermal layer 12, subcutaneous layer 12 a, andtheir respective α's.

[0096] Since C₃′ is a function of the interrelated photon flux densitiesC₁ and/or C₂ and if Xb′₁ does not equal Xb′₂, then the slope C₃′ willnot be nulled out by the Xb′ monitors mentioned. Therefore, Xb₂′ must begreater than Xb₁′. Then the pressure or piezo monitors will compensatecorrectly. The circular pressure balloon is ideal for not only sensingthe change in a pressure, but also providing a pressure against thedermis causing Xb₁′ to be small. However, recognizing that thepenetration depth of the 800 nm light typically extends through dermallayer 12 into the deep tissue, subcutaneous layer 12 a, a differentwavelength selection is appropriate. Thusly, when the photons onlypenetrate into the dermal layer 12, C₃′ will only be a function of z₁and α₁. Those selected wavelengths, as mentioned in U.S. Pat. No.5,372,136, would be the green (570-595 nm) wavelength and 1300 nmwavelength. The green wavelengths are used as the hematocrit bearingwavelength and the 1300 nm wavelength is used as the non-hematocritbearing, or reference wavelength. That is, for reflectance measurementsthe green (Gr)-1300 wavelength pair would give the hematocritinformation as:${\frac{\Delta \quad {{Gr}/{Gr}}}{\Delta \quad {1300/1300}} \cdot \frac{\alpha_{Gr}}{\alpha_{1300}}} = {f({HCT})}$

[0097] III. Methods of $\frac{\partial X_{b}}{\partial t}$

[0098] measurement

[0099] ∂X_(b)/∂t can be measured and compensated for through the use ofa number of different methods—(a) a pressure transducer, (b) a straintransducer such as piezo electric film or strain gage, (e) a differentwavelength of light, such as 1300 nm, which also holds ∂X_(b)/∂tinformation, but holds little hematocrit information, or (d) othertransducers. The individual methods of obtaining ∂X_(b)/∂t are addressedbelow.

[0100] A. Pressure Transducer Measurement of$\frac{\partial X_{b}}{\partial t}$

[0101] Consider a pressure transducer system 36 with a gas filledbladder 38 surrounding a finger tip 10 of a patient contained within afixed volume clam shell fixture 6, see FIGS. 1, 1A-1D. The samederivations, equations, and results would apply to any other bodyappendage or tissue that could be contacted such that a change in thetissue volume would change the pressure of the contacted pressuretransducer system. For a finger note:

V _(clam) =V _(sys) +V _(ƒ)  (23)

[0102] where

[0103] V_(clam)=Clam-shell fixture volume

[0104] V_(sys)=Bladder system volume

[0105] V_(ƒ)=Finger volume

[0106] Also ΔV_(ƒ)=−ΔV_(sys). The system will have a bulk modulus ofelasticity, β, such that: $\begin{matrix}{\frac{\Delta \quad V_{sys}}{V_{sys}} = {{- \frac{\Delta \quad P_{sys}}{\beta}} = {- \frac{\Delta \quad V_{f}}{V_{sys}}}}} & (24)\end{matrix}$

[0107] Substituting (23) into (24) results in: $\begin{matrix}{{\frac{\Delta \quad V_{f}}{V_{f}} = {\left( {\frac{V_{clam}}{V_{f}} - 1} \right)\frac{\Delta \quad P_{sys}}{\beta}}}\begin{matrix}{{{Since}\quad \Delta \quad V_{f}} = {\Delta \quad V_{b}\quad {then}\quad {from}\quad (25)\quad {we}\quad {have}\text{:}}} & \quad \\{\frac{\partial X_{b}}{{\partial t}\quad} = {\left( {\frac{V_{clam}}{V_{f}\quad} - 1} \right)\frac{\Delta \quad P_{sys}}{\beta}}} & \text{(25a)}\end{matrix}} & (25)\end{matrix}$

[0108] As stated above, β is a constant of the pressure transducersystem. However, an empirical solution for$\left( {\frac{V_{clam}}{V_{f}} - 1} \right)$

[0109] was found to have a nonlinear relation to the pressure of thetransducer system. For a given clam shell-pressure transducer embodimenta polynomial, F(p), can accurately describe$\left( {\frac{V_{clam}}{V_{f}} - 1} \right),$

[0110] see FIG. 5

[0111] B. Strain Transducer (Strain Gage/Piezo Electric Film)Measurement of $\frac{\partial X_{b}}{\partial t}$

[0112] Again it is assumed that ΔV_(b)=ΔV₇₁ , and that the fingerchanges volume only by a change in diameter. A strain gage or piezoelectric film is secured tightly around the finger (again any applicablebody appendage or tissue would apply) such that a change in diameterwould produce a strain in the transducer. Specifically assuming acylindrical finger: $\begin{matrix}{\frac{\partial V_{b}}{\partial t} = {\frac{\partial V_{f}}{\partial t} = {\frac{\partial\left( {\pi \quad {zr}^{2}} \right)}{\partial t} = {2\pi \quad {zr}\frac{\partial r}{\partial t}}}}} & (26)\end{matrix}$

[0113] Normalizing with respect to V₇₁ yields: $\begin{matrix}{\frac{\partial X_{b}}{\partial t} = {\frac{\frac{\partial V_{b}}{\partial t}}{V_{total}} = {\frac{2\pi \quad {zr}\frac{\partial r}{\partial t}}{\pi \quad {zr}^{2}} = {\frac{2}{r}\frac{\partial r}{\partial t}}}}} & (27)\end{matrix}$

[0114] A change in the length of the transducer element is related to achange in finger radius by ΔL=2πΔr, therefore: $\begin{matrix}{\frac{\partial X_{b}}{\partial t} = {{2\frac{{\partial L_{t}}/{\partial t}}{L_{t}}} = {2{\gamma (t)}}}} & (28)\end{matrix}$

[0115] where ${\gamma (t)} = \frac{{\partial L}/{\partial t}}{L}$

[0116] is the rate of change in the strain as a function of time. For astrain gage this value can be measured from an appropriate electricalcircuit, see FIG. 6, as it is proportional to the rate of change in thegage resistance.

[0117] For a piezo electric film the voltage produced is proportional tothe strain, therefore: $\begin{matrix}{\frac{\partial{Xb}}{\partial t} = {\frac{2}{g_{31}\tau}\frac{\partial{v(t)}}{\partial t}}} & (29)\end{matrix}$

[0118] where, g₃₁ is the piezoelectric coefficient for the stretch axis,τ is the film thickness and v(t) is the open-circuit output voltage.

[0119] C. 1300 nm Light Measurement of$\frac{\partial X_{b}}{\partial t}$

[0120] The selection of the 1300 nm wavelength is based on criteriaestablished in U.S. Pat. No. 5,372,136. The approach here is not tosolve for ∂X_(b)/∂_(t) and substitute into (19) but to ratiometricallyeliminate ∂X_(b)/∂t. In the case of the 1300 nm reference wavelength,the assumptions following equation (12) are no longer valid; i.e.,∂X_(s)/∂t and ∂X_(w)/∂t are not negligible, since water absorption at1300 nm is so large. Hence, for the 1300 nm equations (13), (14) and(15) would result in: $\begin{matrix}\begin{matrix}{\left( \frac{\partial\alpha}{\partial t} \right)_{13} = \quad {\frac{3}{2\alpha}\left\lbrack {{\left\{ {{\left( {{2K} + S} \right)K_{b}} + {KS}_{b}} \right\} \frac{\partial X_{b}}{\partial t}} +} \right.}} \\\left. \quad {{\left\{ {{\left( {{2K} + S} \right)K_{s}} + {KS}_{s}} \right\} \frac{\partial X_{s}}{\partial t}} + {\left\{ {\left( {{2K} + S} \right)K_{w}} \right\} \frac{\partial X_{w}}{\partial t}}} \right\rbrack\end{matrix} & (30)\end{matrix}$

[0121] where, α, and the bulk and material specific K, and S arewavelength (λ) dependent. Recalling that, X_(b)+X_(s)+X_(w)=1, bydefinition, and that: $\begin{matrix}{\frac{\partial X_{b}}{\partial t} = {\frac{\partial X_{s}}{\partial t} = \frac{\partial X_{w}}{\partial t}}} & (31)\end{matrix}$

[0122] By substituting (31) into (30) and noting that K_(w13)≈K_(b13),the following is obtained: $\begin{matrix}{\left( \frac{\partial\alpha}{\partial t} \right)_{13} = {\frac{3}{2\alpha}\left\lbrack {{\left\{ {KS}_{b} \right\} \frac{\partial X_{b}}{\partial t}} + {\left\{ {{\left( {{2K} + S} \right)\left\lbrack {K_{s} - K_{w}} \right\rbrack} + {K_{s}S_{s}}} \right\} \frac{\partial X_{s}}{\partial t}}} \right.}} & (32)\end{matrix}$

[0123] Since,${{\frac{\partial X_{b}}{\partial t}}\frac{\partial X_{s}}{\partial t}},$

[0124] (32) becomes: $\begin{matrix}{\left( \frac{\partial\alpha}{\partial t} \right)_{13} = {\frac{3}{2\alpha_{13}}\left\{ {KS}_{b} \right\}_{13}\frac{\partial X_{b}}{\partial t}}} & (33)\end{matrix}$

[0125] Therefore, to eliminate $\frac{\partial{Xb}}{\partial t}$

[0126] and solve for the hematocrit, (17) is divided by (33) yielding:$\begin{matrix}{\frac{\left( {{\partial\alpha}/{\partial t}} \right)_{8}}{\left( {{\partial\alpha}/{\partial t}} \right)_{13}} = {\frac{\alpha_{13}}{\alpha_{8}}\frac{K_{b_{8}}S_{8}}{K_{13}S_{b_{13}}}}} & (34)\end{matrix}$

[0127] Since S₈ and K₁₃ are well behaved and known (let K₁₃/S₈=G) inhuman tissue and the ratio $\frac{K_{b8}}{S_{b13}}$

[0128] is a function of H, then rearranging (34) gives: $\begin{matrix}{{f(H)} = {\frac{K_{b_{8}}}{S_{b_{13}}} = {\frac{\alpha_{8}}{\alpha_{13}}\frac{\left( \frac{\partial\alpha}{\partial t} \right)_{8}}{\left( \frac{\partial\alpha}{{\partial t}\quad} \right)_{13}}}}} & (35)\end{matrix}$

[0129] Where $\frac{\partial\alpha}{\partial t}$

[0130] can be measured using (11) or (14). See FIG. 7 for ƒ(H).

[0131] D. Other ∂X_(b)/∂t measurements such as doppler, ultrasonic,electrical conductivity, magnetic permeability and other techniques havesimilar derivations. The important consideration is that ∂X_(b)/∂t is anormalized time varying quantity.

[0132] IV. Analytical Implementation

[0133] If hematocrit is constant over a given time interval, averagingcan eliminate system noise whose frequency components have correspondingperiods much shorter than the interval. In addition, by observing thedata variance during the interval it may be determined that the data isinvalid. In the present system, the data acquisition rate isapproximately 1000 data samples per second. This means that within atypical human pulse about 1000 samples of data are available forappropriate numerical analysis, averaging and qualification. Recognizingthat both the intensity of light and the pressure in the transducersystem are changing in time during the influx of blood is of greatimportance. Since the parametric relationship of ∂α/∂t as a function of∂P/∂t (where P is pressure) during the cardiac cycle should be linear, amultiplicity of data points facilitate qualification of the signal foraccuracy and linearity. Whereas, prior techniques involving only thepeak and valley values of the cardiac cycle require numerous pulses toqualify the data set. See FIGS. 8, 9 and 10.

[0134]FIG. 8 shows di/dt/i as well as dP/dt verses time during thecardiac pulse—it is a pulse showing ≈200+ data samples during the pulse.

[0135]FIG. 9 shows (di/dt)/i vs dP/dt showing that within one cardiacpulse 200 plus data samples are linearly related, i.e. trace up out ofthe “0” origin up to a maximum value and then back down toward theorigin again.

[0136]FIG. 10 shows da/dt/dP/dt versus time during one single cardiacpulse with 200 plus samples of data from time 15-45 giving a value ofabout 4.5 thousandths. The data can then be averaged, as if 200+individuals pulse (max-min) values were actually taken as present dayoxymeters do.

[0137] A. Homogeneity

[0138] Since the above derivations are based on the assumption of tissuehomogeneity (i.e.,∂X_(b1)/∂t=∂X_(b2)/∂t, A₁=A₂, ∂A₁/∂X_(b)=∂A₂/∂X_(b),α₁=α₂, etc.), high-speed, single-pulse, multiple parameter samplingallows for mathematical qualification of homogeneity, by requiringlinearity of ln(i) vs. d and (∂i/∂t)/i vs. d. Under these constraintsand when qualified as homogeneous, (∂α/∂t)/(∂P/∂t) also may be assumedto be linear over the entire pulse contour. Finally, both α and ∂α/∂tmust also be linear, further assuring homogeneity in X_(b), and in∂X_(b)/∂t.

[0139] B. Circuitry

[0140] See U.S. Pat. No. 5,372,136 for the operational circuitrydescription, which allows for high speed sampling of the opticalintensities. See FIGS. 6 and 10 for similar circuitry considerations forsampling of pressure, peizo, and strain-gage measurements.

[0141] The circuitry shown and discussed in U.S. Pat. No. 5,372,136 isprogrammable by conventional techniques to solve and implement theequations and calculations presented in this application. FIG. 6 shows apiezo transducer circuit having a transducer 50 connected to a series ofoperational amplifiers, resistors and capacitors in accordance with thefigure. The circuit terminates in an analog output 52 for connection tothe “E” connection shown in the middle left side of FIG. 9D in U.S. Pat.No. 5,372,136. FIG. 11, on the other hand, shows a pressure transducercircuit having a pressure transducer made 62 connected to a series ofoperational amplifiers, a capacitor, resistors and variable resistors asshown in the figure. The circuit terminates in an analog output alsoconnected to the aforementioned “E” connection.

[0142] Referring more specifically to FIG. 6, a crystal oscillator isconnected to ground and to the non-inverting input of a firstoperational amplifier, which may be an LM158. The non-inverting input ofthe first operational amplifier is connected to ground by a 0.047 μFcapacitor C3. The first operational amplifier's feedback path to itsinverting input includes a 470 K resistor R8. The first operationalamplifier is suitably biased at the junction of a 220 Ω resistor R7 anda 150 μF capacitor C4 that are connected between VCC and ground.

[0143] A second operational amplifier, which may also be an LM 158,receives the output of the first operational amplifier at its invertinginput via a 10 KΩ resistor R5. The second operational amplifier'snon-inverting input is connected to several locations:

[0144] to a voltage VB51, which may be 4.096 volts, through a 10 KΩresistor R2;

[0145] to a middle node of a voltage divider, the voltages dividerextending between the non-inverting input of the first operationalamplifier via a 10 MΩ resistor R4 to the middle node, and via a 10 KΩresistor R1 to ground;

[0146] to the inverting input of the first operational amplifier via a10 KΩ resistor R9; and

[0147] to ground via a 220 μF capacitor C5.

[0148] The second operational amplifier's feedback path to its invertinginput includes a parallel arrangement of a 0.1 μF capacitor C2 and a 47KΩ resistor R6. The second operational amplifier drives the A/D output52 via a 10 KΩ resistor R3, the output connected to ground via a 1 μFcapacitor C1.

[0149] Of course, the particular choice, arrangement and values ofcomponents shown in FIG. 6 may be varied while still remaining withinthe scope of the invention.

[0150] Referring now to FIG. 10, first through fourth operationalamplifiers, which may be LM348s, are illustrated. The operationalamplifiers are powered and biased by voltages VCC and VEE.

[0151] The first operational amplifier's non-inverting input is set to avalue determined by the tap setting of a 1 KΩ adjustable resistor R2that extends between VCC and VEE. The DAC input drives the firstoperational amplifier's inverting input via a 1 KΩ resistor R1. Thefirst operational amplifier's feedback path includes a 50 KΩ adjustableresistor R4. The first operational amplifier drives the secondoperational amplifier's inverting input through an 11 KΩ resistor R3.The feedback path to the inverting input of the second operationalamplifier includes a 100 Ω resistor R5.

[0152] A transducer 62, which may include a Motorola MPX20100P, hasopposite terminals that drive the non-inverting inputs of the second andthird operational amplifiers, respectively. The other two oppositeterminals of the transducer are connected to VCC and ground,respectively.

[0153] The second operational amplifier drives the inverting input ofthe third operational amplifier via a 750 Ω resistor R6. The thirdoperational amplifier's feedback path to its inverting input includes aparallel arrangement of a 93.1 KΩ resistor R10 and a 0.001 μF capacitorC1.

[0154] The third operational amplifier drives the non-inverting input ofthe fourth operational amplifier via a 1 KΩ resistor R7. The invertinginput of the fourth operational amplifier is connected to ground via a 1KΩ resistor R8. The feedback path to the inverting input of the fourthoperational amplifier includes a 50 KΩ adjustable resistor R9. Thefourth operational amplifier drives the output of the FIG. 11 circuit.

[0155] Of course, the particular choice, arrangement and values ofcomponents shown in FIG. 10 may be varied while still remaining withinthe scope of the invention.

[0156] C. Preferred Embodiment

[0157] Physical embodiments as shown in FIG. 1 include the opticalarray, pressure transducer/balloon system and clam-shell fixture.Requisites of the preferred embodiment include a holder for the finger(or other tissue) such as seen in FIGS. 1 and 1A and 1B. This clam-shellfixture not only secures the tissue but also the optical array, andtransducer system.

[0158]FIG. 1D is a schematic diagram for a mylar base member 38 that isshaped generally like a cross. As oriented in FIG. 1D, verticallyextending portion 52 crosses with a horizontally extending portion 54 toyield top leg 56, bottom leg 58, and side legs 60, 62. In use, a finger7 lies along the longitudinally extending portion 52 with the finger tipplaced on the top leg 56 to properly cover the arrangement of LED's 32and photodetector 34, which are arranged like those on FIGS. 1A-1C. Apiezoelectric pressure transducer or strain gage 66 spans thehorizontally extending portion 54 from near the tip of side leg 60 tothe tip of side leg 62. In this orientation, the transducer or gage maybe wrapped around the finger 7 for use in measurements.

[0159] The optical array 30, seen in FIG. 1D, shows the arrangement ofmultiple LED's 32 spaced at known separation distances from the detector34. This array provides for the instantaneous distance, or “d”,derivative, by the transmission mode shown in FIG. 1A or in reflectancemodes shown in FIGS. 1B and 1C. However, as shown in FIG. 1E, a singleLED 42 swept across the finger 7 or tissue surface 9 with a steppermotor 44 would provide a d derivative as would a cantilevered clam-shellwith an angular measurement device. In any case, d must be known and/orfixed. Also the detectors and emitters may be placed anywhere about thefinger.

[0160] The pressure/balloon, strain gage, or peizo transducer systemincorporated within the clam-shell fixture (see Section III, A, B, C andFIG. 1A) provides the contact surface area needed to define the∂X_(b)/∂t.

[0161] High-speed sampling provides for a closer approximation of theinstantaneous time, t, derivative, ∂/∂t, as opposed to peak-valleyvalues, see FIG. 8. Therefore, the above embodiments allow for thedirect measurement of ln(i) at d₁, d₂, d₃ and d₄ cotemporaneously,thereby determining the actual α of the sampled tissue. Likewise(∂i/∂t)/i can be directly measured at d₁, d₂,, d₃ and d₄,cotemporaneously during the pulse which determines the instantaneous∂α/∂t.

[0162] The above mentioned optical array can be utilized transmissivelyand/or reflectively provided the separation distance between thedetector and first emitter (d₁) is greater than 3 mm.

[0163] D. Choice of Non-Ionizing Wavelengths

[0164] Since hematocrit is an example of the desired biologicalconstituent concentration value of interest, selection criteria of thepreferred wavelength must include an understanding of equation (5). Thatis, a wavelength whose coefficients K_(s), K_(w), K_(p) are smallcompared to K_(b) and which are also insensitive to oxygen saturationstatus must be selected. Such wavelengths include 805 nm, 590 nm, 569 nmand other isobestic wavelengths with negligible water absorption. Whilenon-isobestic wavelengths, with small water absorption, could function,a second wavelength is needed to null out the oxygen saturation effects.

[0165] If the desired biologic constituent value of interest is theblood glucose, bilirubin, cholesterol or other parameters, then a secondwavelength must be chosen. The first wavelength, 805 nm, is used tomeasure the hematocrit, H, after which a K_(p805) (the absorbance ofplasma at λ=805 nm) can be determined. Then, knowing the H, a secondwavelength, 570 nm, is chosen where K_(p570) is less than K_(p805).Similarly, if the first wavelength used to measure the H and thereference glucose, K_(p) (glucose) is 570 nm, the second wavelength,1060 nm, is chosen where K_(p570) is much less than K_(p1060). In thecase of bilirubin, the first wavelength used to measure the H and thereference bilirubin, K_(p) (bilirubin), is 570 nm, the secondwavelength, 440 nm, is then chosen when K_(p570) is much less thanK_(p440). The selection of these above mentioned wavelengths thereforeassures uniqueness for the measurement of the desired biologicconstituent.

[0166] Additionally for glucose determination, recall that the 1300 nmwavelength is not hematocrit or hemoglobin dependent but will be glucosesensitive. This is primarily due to the dependence of the scatteringcoefficient on the difference between the index of refraction of purewater and glucose, i.e.: recall

[0167] S_(b8)=H (1−H) σ_(s8) (from equation 7) where:

σ_(s8)=8π²ρ₀ ²(ρ′₈−1)² ·b ^(v)/λ²

[0168] where ρ′₈=index of refraction of the RBC hemoglobin at 800 nmrelative to plasma ρ₀ (the plasma index of refraction), and,

[0169] S_(b13)=H (1−H) σ_(s13) (also from equation 7) where:

σ_(s13)=8π²ρ₀ ²(ρ′₁₃−1)² ·b ^(v)/λ²

[0170] ρ′₁₃=the index of refraction of glucose at 1300 nm relative toρ₀.

[0171] Therefore, the 8 13 ratio has both hematocrit and glucoseinformation. Whereas the α₈·α′₈/ΔP (equation 18a) ratio has onlyhematocrit information. Therefore the differential combination of thoseratios will be a strong function of glucose only.

[0172] E. Improved Accuracy Pulse Oximeter Device

[0173] The accuracy of present day pulse oximeters suffers from 4 majorproblems: tissue perfusion (low X_(b) and low ∂X_(b)/∂t), d dependence(varying finger sizes), tissue nonhomogeneity (the tissue penetrationdepth for 660 nm light is not the same as for 940 nm light), and Hdependence (see equation (5)).

[0174] All of the above mentioned deficiencies in pulse oximetry can beeliminated by understanding equation (13). Equation (13) indicates an“offset term”, ${- \frac{1}{A}}{\frac{\partial A}{\partial X_{b}}.}$

[0175] Hence, while merely dividing (Δi/i)_(λ1) by (Δi/i)_(λ2) mitigatesthe effect of ∂X_(b)/∂t, the d's do not completely cancel, therebyyielding the above mentioned problems. To improve pulse oximeteraccuracy, a derivative is needed as in (14), which eliminates the“offset term”. Hence, the ratio of (∂α/∂t)₈₀₅/(∂α/tt)₆₆₀ results in noH, d, or X_(b) dependence and the use of the multiple LED array andhigh-speed sampling as mentioned in section IV qualifies the tissue ashomogeneous.

[0176] V. A Simplified Two Step Approach

[0177] (A) Determination of H and X_(b)

[0178] The bulk attenuation coefficient, α, can be easily measured withthe optical array, at 805 nm, utilizing equation (10) and as describedin Section IV(C). Notice that at 805 nm, α is a strong function of H andX_(b) since K_(s8)K_(w8), K_(p8) are small, see FIG. 12.

[0179] Therefore, by knowing X_(b) itself, H can be determined. X_(b)itself can be determined using a strain gage in the following two stepapproach. Step One, measure the strain gage resistance when the fingeris made bloodless, by squeezing finger, such as with a stepper motor.Step Two, measure the strain gage resistance when the finger is bloodfilled, for example by suction. Mathematically, at 805 nm and whenK_(s), K_(p), K_(w), are small, equation (3) is approximated by:

α²≈3KS  (36)

[0180] or

α²≈3[K _(b) X _(b) ][S _(b) X _(b) +S _(s) X _(s)]  (37)

[0181] Substituting (5) and (7) into (37) yields: $\begin{matrix}{0 = {{{3\left\lbrack {H\frac{\sigma_{a}}{V}X_{b}} \right\rbrack}\left\lbrack {{{H\left( {1 - H} \right)}\left( {1.4 - H} \right)\frac{\sigma_{s}}{V}X_{b}} + {S_{s}X_{s}}} \right\rbrack} - \alpha^{2}}} & (38)\end{matrix}$

[0182] With X_(b) and α measured and known, and with the σ's and S_(s),X_(s) approximately constant, H can be solved with a quadratic formulaor a polynomial fit.

[0183] The strain gage determination of X_(b) is as follows:

[0184] Let V_(o)=the volume of a bloodless finger. Let V_(ƒ)=the volumeof blood filled finger, and again considering the finger as a cylinder:

V _(o) =πr ² z=V _(s) +V _(w)  (39)

V _(ƒ) =πR ² z=V _(b) +V _(s) +V _(w)  (40)

[0185] and $\begin{matrix}{\frac{V_{o}}{V_{f}} = \left( \frac{r}{R} \right)^{2}} & (41)\end{matrix}$

[0186] From equation (20) $\begin{matrix}{X_{b} = {\frac{V_{f} - V_{o}}{V_{f}} = {1 - \frac{V_{a}}{V_{f}}}}} & (42)\end{matrix}$

[0187] Substituting (41) into (42): $\begin{matrix}{X_{b} = {1 - \left( \frac{r}{R} \right)^{2}}} & (43)\end{matrix}$

[0188] Where the strain gage resistances are proportional to the radius,r and R, of the finger.

[0189] (B) Determination of Tissue Water Content X_(w)

[0190] Choosing the wavelength of 1300 nm, where K_(s) and K_(w) aresignificant, the tissue water content, X_(w), can be determined. Recallthat 1−X_(b)−X_(w)=X_(s) and substituting into (3) yields:

₁₃ ² ₁₃=3({K _(b) −K _(s) }X _(b) +{K _(w) −K _(s) }X _(w) +K_(s))  (44)

([{K _(b) −K _(s) }+{S _(b) −S _(s) }]X _(b) +[{K _(w) −K _(s) }−S _(s)]X _(w)+(K _(s) +S _(s)))

[0191] With α₁₃,, X_(b) and H determined and because K_(b), K_(s),K_(w), S_(b), and S_(s) are known coefficient values at 1300 nm, X_(w)is solved with either a quadratic formula or a polynomial fit.

RESULTS

[0192]FIG. 13 demonstrates preliminary results with 30 patients theapplication of the method and apparatus and the application of Equation19 on numerous patients with a correlation of r=0.96. As impliedthroughout, those skilled in the art will also appreciate that themethods for determining blood hematocrit values within the scope of thepresent invention may be adapted for determining other non-hematocritbiologic constituent values such as glucose, bilirubin, cholesterol,tissue water, etc.

[0193] The present invention may be embodied in other specific formswithout departing from its spirit or essential characteristics. Whilethe foregoing described embodiments are to be considered in all respectsonly as illustrative of the claimed invention, they are not intended torestrict the scope of the claims. The scope of the invention is,therefore, indicated by the following appended claims rather than by theforegoing description. All changes within the meaning and range ofequivalency of the claims are to be embraced within their scope.

What is claimed is:
 1. A method for determining a desired biologicconstituent concentration of the blood of a patient, the blood flowingin a pulsatile fashion in a body part of the patient so as to besubjectable to transcutaneous examination in the body part, the bodypart defining a blood conduit and the method comprising the steps of:(a) placing the blood conduit within a blood conduit receiver with theblood flowing in the blood conduit; (b) directing radiation into theflowing blood within the blood conduit using a radiation generatorsituated within said blood conduit receiver means, said radiationdefining a directed radiation comprising a first quantity of radiationat a radiation wavelength which, when directed into the flowing bloodwithin the blood conduit, (A) has a first attenuation value which varieswith the desired biologic constituent concentration in the flowing bloodand (B) has a second attenuation value which varies with theconcentration of components other than the desired biologic constituentin the flowing blood, which second attenuation value is at least tentimes smaller than said first attenuation value, and (c) detecting theportion of said directed radiation which passes through both the bloodconduit and the flowing blood therein using a radiation detectorsituated within said blood conduit receiver, said detected portion ofsaid directed radiation comprising a second quantity of radiation at theradiation wave length; and (d) detecting energy from the flowing bloodwithin the blood conduit using an energy transducer situated within saidblood conduit receiver, said energy defining a transduced energycomprising a quantity of energy which when detected from the flowingblood within the blood conduit, has a value which varies with thenormalized change of the pulsatile blood; and (e) operating exclusivelyon the second quantities of the radiation and the transduced energy todetermine the desired biologic constituent concentration.
 2. A method asdefined in claim 1 , wherein the step of detecting the second quantityof the radiation wavelength comprises the steps of: (a) determining theintensity of the total radiation wavelength; and (b) determining aradiation wavelength pulsatile value representing the intensities of apulsatile component of the radiation wavelength at discreet timeintervals during the pulse.
 3. A method as defined in claim 1 , whereinthe step of detecting the transduced energy comprises the steps of: (a)determining the electronic signal generated from the transduced energy;and (b) determining a transduced energy pulsatile value representing theintensities of a pulsatile component of the transduced energy atdiscreet time intervals during the pulse.
 4. A method as defined inclaim 1 , wherein the step of operating exclusively on the secondquantities of the radiation at the radiation wavelength to determine thedesired biologic constituent concentration of the patient comprises thesteps of: (a) mathematically operating on the second quantities of theradiation wavelength such that the time derivative of the pulsatileintensities is normalized by the average intensity over the pulseinterval followed by a distance derivative of that quantity to produce avalue proportional to ∂α/∂t; and (b) mathematically operating on thesecond quantities of the radiation wavelength such that the logarithm ofthe intensity is distance differentiated to produce the value α.
 5. Amethod as defined in claim 1 , wherein the step of operating exclusivelyon the transduced energy comprises the step of performing the timederivative of the normalized pulsatile transduced energy to obtain thevalue ∂X_(b)/∂t.
 6. A method as defined in claim 1 , wherein the step ofoperating exclusively on the second quantities of the radiation and thetransduced energy comprises the step of mathematically solving therelationship K_(b)=B·(α·∂α/∂t)/(∂X_(b)/∂t) with a polynomial function orempirically determined value.
 7. A method as defined in claim 1 ,wherein the desired biologic constituent comprises hematocrit orhemoglobin.
 8. A method as defined in claim 1 , wherein the firstattenuation value is substantially the same amount for oxyhemoglobin andfor reduced hemoglobin in the flowing blood and the second attenuationvalue is at least ten items smaller than said first attenuation valuefor any competing constituent in the flowing blood.
 9. A method asdefined in claim 1 , wherein the radiation wavelength is in the rangefrom about 790 nanometers to 850 nanometers.
 10. A method as defined inclaim 1 , wherein the radiation wavelength is in the range from about550 nanometers to 600 nanometers.
 11. A method as defined in claim 1 ,wherein the energy transducer means is a pressure transducer element, astrain gage element, a piezo electric film element, or a dopplerdetection element.
 12. A method for determining a desired biologicconstituent concentration of the blood of a patient, the blood flowingin a pulsatile fashion in a body part of the patient so as to besubjectable to transcutaneous examination in the body part, the bodypart defining a blood conduit and the method comprising the steps of:(a) placing the blood conduit within a blood conduit receiver with theblood flowing in the blood conduit; (b) directing radiation into theflowing blood within the blood conduit using a radiation generatorsituated within said blood conduit receiver, said radiation defining adirected radiation comprising: (i) a first quantity of radiation at aradiation wavelength which, when directed into the flowing blood withinthe blood conduit, (A) has a first attenuation value which varies withthe desired biologic constituent concentration in the flowing blood and(B) has a second attenuation value which varies with the concentrationof components other than the desired biologic constituent in the flowingblood, which second attenuation value is at least ten times smaller thansaid first attenuation value, and (ii) a first quantity of a radiationat a second radiation wavelength, distinct from said first wavelength,which, when directed into the flowing blood within the blood conduit,(A) has a third attenuation value which for varying concentrations inthe flowing blood of the desired blood constituent is a non-fixedmultiple of said first attenuation value; and (B) has a fourthattenuation value which varies with the concentration of componentsother than the desired biologic constituent in the flowing blood, whichfourth attenuation value is at least ten times greater than said secondattenuation value; (c) detecting the portion of said directed radiationwhich passes through both the blood conduit and the flowing bloodtherein using a radiation detector situated within said blood conduitreceiver, said detected portion of said directed radiation comprising:(i) a second quantity of a radiation at the first radiation wavelengthand, (ii) a second quantity of a radiation at the second radiationwavelength; (d) detecting energy from the flowing blood within the bloodconduit using an energy transducer situated within said blood conduitreceiver, said energy defining a transduced energy comprising a quantityof energy which when detected from the flowing blood within the bloodconduit, has a value which varies with the normalized change of thepulsatile blood; and (e) operating exclusively on the second quantitiesof the radiations and the transduced energy to determine the desiredbiologic constituent concentration.
 13. A method as defined in claim 12, wherein the step of operating exclusively on the transduced energycomprises the step of performing the time derivative of the normalpulsatile transduced energy of the second radiation wavelength asdefined in claim 19 to obtain the value ∂X_(b)/∂t.
 14. A method asdefined in claim 12 , wherein the step of operating exclusively on thesecond quantities of the radiation and the transduced energy comprisesthe step of solving the relationship ƒ(H)=G·(α·(∂α/∂t))first/(α·(∂α/∂t)) second with a polynomial function or empiricallydetermined value.
 15. A method for determining a desired biologicconstituent concentration of the blood of a patient, the blood flowingin a pulsatile fashion in a body part of the patient so as to besubjectable to transcutaneous examination in the body part, the bodypart defining a blood conduit and the method comprising the steps of:(a) placing the blood conduit within a blood conduit receiver with theblood flowing in the blood conduit; (b) directing radiation into theflowing blood within the blood conduit using a radiation generatorsituated within said blood conduit receiver, said radiation defining adirected radiation comprising a first quantity of a radiation at aradiation wavelength which, when directed into the flowing blood withinthe blood conduit, (A) has a first attenuation value which varies withthe desired biologic constituent concentration in the flowing blood and(B) has a second attenuation value which varies with the concentrationof components other than the desired biologic constituent in the flowingblood, which second attenuation value is at least ten times smaller thansaid first attenuation value; (c) detecting the portion of said directedradiation which passes through both the blood conduit and the flowingblood therein using a radiation detector situated within said bloodconduit receiver, said detected portion of said directed radiationcomprising a second quantity of radiation at the radiation wavelength;and (d) detecting energy from the flowing blood within the blood conduitusing an energy transducer situated within said blood conduit receiver,said energy defining a transduced energy comprising a quantity of energywhich when detected from the flowing blood within the blood conduit, hasa value which varies with the normalized blood volume; and (e) operatingexclusively on the second quantity of the radiation and the transducedenergy to determine the desired biologic constituent concentration. 16.A method as defined in claim 15 , wherein the step of operatingexclusively on the transduced energy comprises the step of measuring thetransduced energy when the blood conduit is blood-filled, then latermade blood-less in order to obtain the value X_(b).
 17. A method asdefined in claim 16 , wherein the step of determining X_(b) isaccomplished by solving 1−(V_(d)/V_(ƒ)) with the above energy transducermeans.
 18. A method as defined in claim 17 , wherein the step ofdetermining V_(o)/V_(ƒ) is accomplished by solving (V_(c)/V_(ƒ))−1 witha polynomial function of the pressure transducer element.
 19. A methodfor determining a desired biologic constituent concentration of theblood of a patient, the blood flowing in a pulsatile fashion in a bodypart of the patient so as to be subjectable to transcutaneousexamination in the body part, the body part defining a blood conduit andthe method comprising the steps of: (a) placing the blood conduit withina blood conduit receiver with the blood flowing in the blood conduit;(b) directing radiation into the flowing blood within the blood conduitusing a radiation generator situated within said blood conduit receiver,said radiation defining a directed radiation comprising: (i) a firstquantity of a radiation at a radiation wavelength which, when directedinto the flowing blood within the blood conduit, (A) has a fifthattenuation value which greatly varies with the nondesired biologicconstituent concentration in the flowing blood and (B) has a sixthattenuation value which varies with the concentration of the desiredbiologic constituent in the flowing blood, which second attenuationvalue is at least ten times smaller than said fifth attenuation value,and (ii) a first quantity of a radiation at a second radiationwavelength, distinct from said first wavelength, which, when directedinto the flowing blood within the blood conduit, (A) has a seventhattenuation value which for varying concentrations in the flowing bloodof the nondesired blood constituent is a multiple of said fifthattenuation value; (B) has an eighth attenuation value which varies withthe concentration of the desired biologic constituent in the flowingblood, which eighth attenuation value is at least five times greaterthan said sixth attenuation value; (c) detecting the portion of saiddirected radiation which passes through both the blood conduit and theflowing blood therein using a radiation detection means situated withinsaid blood conduit receiving means, said detected portion of saiddirected radiation comprising: (i) a second quantity of a radiation atthe first radiation wavelength, and (ii) a second quantity of aradiation at the second radiation wavelength; (d) detecting energy fromthe flowing blood within the blood conduit using an energy transducermeans situated within said blood conduit receiving means, said energydefining a transduced energy comprising a quantity of energy which whendetected from the flowing blood within the blood conduit, has a valuewhich varies with the normalized change of the pulsatile blood; and (e)operating exclusively on the second quantities of the radiations and thetransduced energy to determine the desired biologic constituentconcentration.
 20. A method for determining a desired biologicconstituent concentration of the blood of a patient, the blood flowingin a pulsatile fashion in a body part of the patient so as to besubjectable to transcutaneous examination in the body part, the bodypart defining a blood conduit and the method comprising the steps of.(a) placing the blood conduit within a blood conduit receiver means withthe blood flowing in the blood conduit: (b) directing radiation into theflowing blood within the blood conduit using a radiation generatorsituated within said blood conduit receiver, said radiation defining adirected radiation comprising a first quantity of a radiation at aradiation wavelength which, when directed into the flowing blood withinthe blood conduit, (A) has a first attenuation value which varies withthe desired biologic constituent concentration in the flowing blood and(B) has a second attenuation value which varies with the concentrationof components other than the desired biologic constituent in the flowingblood, which second attenuation value is at least ten times smaller thansaid first attenuation value; (c) detecting the portion of said directedradiation which passes through both the blood conduit and the flowingblood therein using a radiation detector situated within said bloodconduit receiver, said detected portion of said directed radiationcomprising a second quantity of a radiation at the radiation wavelength;and (d) detecting energy from the flowing blood within the blood conduitusing an energy transducer situated within said blood conduit receiver,said energy defining a transduced energy comprising a quantity of energywhich when detected from the flowing blood within the blood conduit, hasa value which varies with the normalized change of the pulsatile blood;(e) operating exclusively on the second quantities of the radiations andthe transduced energy to determine the desired biologic constituentconcentration by qualifying the tissue's homogeneity from the linearityof the distance differentiation.
 21. A method as defined in claim 20 ,wherein the step of operating exclusively on the second quantities ofthe radiation at the radiation wavelength to determine the desiredbiologic constituent concentration of the patient comprises the stepsof: (a) mathematically operating on the second quantities of theradiation wavelength such that the time derivative of the pulsatileintensities is normalized by the average intensity over the pulseinterval followed by a distance derivative of that quantity to produce avalue proportional to ∂α/∂t; (b) mathematically operating on the secondquantities of the radiation wavelength such that the logarithm of theintensity is distance differentiated to produce the value α; (c)mathematically determining the linearity and deviation of the logarithmof the intensity and the (∂i/∂t)/i values versus distance; and (d)mathematically decoupling, isolating, and determining the individualconstituent absorptive and scattering coefficients from the homogeneityqualified α, ∂α/∂t and ∂X_(b)/∂t values.